I am trying to hookup a standard track light to a light point - standard 3 wire, 120volt. (black, green and white wiring) on the light. When testing the wiring, there is power on the hot black wire. When hooking up the light, there is suddenly no power on the wire that was hot.

There is some strange setup with the switches in the room with this light point.

Switch 1 - turns on an exterior light.
Switch 2 - turns on an interior light
Switch 3 - doesn't appear to do much.

When either switch 1 or switch 2 are turned on, there is power to this light point, except when the light is connected. When switch 1 and switch 2 are off, there is never power flowing to this light. Switch 3 doesn't appear to do much itself.

This is in a rental house - I'm wondering what is going on with the lighting because I've tried to connect 2 different lights to ensure it wasn't a light problem and I always lose power upon connecting a light.

Not sure if anyone has any suggestions on how to resolve.

Because this is a rental property your hands are tied if you are the renter.

Most local codes will not allow DIY work on rental property.

Licensed electricians and possibly the landlord are allowed to fix the failure.

Personally, I would get a licensed electrican rather then trust an unknown handyman or landlord to do the work.